Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page vii
... tensor as seeming to me to express most clearly what is meant . After treating of proportion I have not hesitated to employ those special ratios known as trigonometric func- tions in deducing geometric relations . In the earlier parts ...
... tensor as seeming to me to express most clearly what is meant . After treating of proportion I have not hesitated to employ those special ratios known as trigonometric func- tions in deducing geometric relations . In the earlier parts ...
Page 148
... tensor of AB with respect to CD . ( Hamilton . ) As far as two segments are concerned , the tensor , as a numerical quantity , is identical with the ratio of the segments , but it introduces a different idea . Hence in the case of com ...
... tensor of AB with respect to CD . ( Hamilton . ) As far as two segments are concerned , the tensor , as a numerical quantity , is identical with the ratio of the segments , but it introduces a different idea . Hence in the case of com ...
Page 149
... tensor will bring AB to AC . Let BD be divided into 10 equal parts whereof E and F are those numbered 4 and 5 . Then the tensor 1.4 stretches AB to AE , and tensor 1.5 stretches AB to AF . But the first of these is too small and the ...
... tensor will bring AB to AC . Let BD be divided into 10 equal parts whereof E and F are those numbered 4 and 5 . Then the tensor 1.4 stretches AB to AE , and tensor 1.5 stretches AB to AF . But the first of these is too small and the ...
Page 150
... tensor of the segment AB with respect to AC , or the tensor of AB on AC is the numerical factor which brings AC to AB . But according to the operative principles of Algebra , AB AC AB . AC = AB , AC is the tensor which brings AC to AB ...
... tensor of the segment AB with respect to AC , or the tensor of AB on AC is the numerical factor which brings AC to AB . But according to the operative principles of Algebra , AB AC AB . AC = AB , AC is the tensor which brings AC to AB ...
Page 157
... tensors of every pair of corresponding line segments , one from each figure , are equal , and hence that any two or more line- segments from one figure are proportional to the correspond- ing segments from the second figure . Def ...
... tensors of every pair of corresponding line segments , one from each figure , are equal , and hence that any two or more line- segments from one figure are proportional to the correspond- ing segments from the second figure . Def ...
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Common terms and phrases
ABCD Algebra altitude becomes bisects c.p.-circles centre of similitude chord of contact circles touch circumcircle co-axal coincide collinear concurrent concurrent lines concyclic congruent cut the circle denote diagonals diameter divided double points end-points equal angles equianharmonic equilateral triangle excircles external bisector fixed point geometric given circles given line given point harmonic range Hence hexagram homographic homologous hypothenuse incircle internal angles inverse points isosceles joins LAOB line-segment locus median middle point nine-points circle opposite sides orthogonally pair parallel parallelogram passes pencil perpendicular perspective plane point of contact point of intersection polar reciprocal Proof quadrangle radical axis radical centre radii radius rectangle rectilinear figure regular polygon rhombus right angle right bisector rotation secant similar Similarly square straight angle symbol tangent tensor theorem Theorem.-The three circles transversal vertex vertices